Massachusetts consumers may soon get reassurance that the fish they order in restaurants is actually what ends up on their plates.

A State House hearing on food safety on Tuesday included discussion about a bill that would fine supermarkets and restaurants that mislabel certain seafoods and ban the sale of escolar, an oily species that is often sold under a different name in sushi restaurants.

“Consumers deserve to have full and accurate information where seafood comes from,’’ said Beckie Zisser, Ocean advocate for Oceana, a nonprofit group that has revealed widespread seafood fraud across the country.

Zisser spoke at the hearing, which included a range of bills relating to food safety.

According to the proposed legislation that addresses seafood mislabeling, businesses caught misrepresenting fish such as Atlantic cod, Atlantic halibut, red snapper, or gray sole could face fines of up to $800 and have their licenses to operate suspended or revoked after repeat offenses.

Restaurants caught serving escolar, frequently mislabeled as white tuna or albacore at sushi restaurants, could be fined. Albacore, a white tuna with a mild taste, is not related to escolar and costs more.

Another bill, while not directly addressing mislabeling, would also help to ensure that consumers receive the seafood they order by requiring better labeling on saltwater fish to spell out risks from mercury and other toxins.

“From our perspective, any information is better,’’ Zisser said.

While a system that tracks fish from boat to dinner plate is still needed, she said, the bills “are a good first step.”